Memory effects in nonlinear transport: kinetic equations and ratchet devices

We present a new method to derive kinetic equations for systems undergoing non-linear transport in the presence of memory effects. In the framework of mesoscopic nonequilibrium thermodynamics, we derive a generalized Fokker-Planck equation incorporating memory effects through time-dependent coefficients. As applications, we first discuss the non-Markovian dynamics of anomalous diffusion in a potential, analyzing the validity of the fluctuation-dissipation theorem. In a second application, we propose a new ratchet mechanism in which the periodic driving acting on the particle is induced by the Onsager coupling of the diffusion current with an oscillating thermodynamic force.